Inventory control and price discount policies for perishable products with age and price-dependent demand

Document Type : Article

Authors

Department of Industrial Engineering, Babol Noshiravani University of Technology, Babol, 47148-71167, Iran

Abstract

In this paper, the inventory control and price discount problem for perishable products with price and age-dependent demand is investigated. The seller adjusts prices to influence demand and optimize profits through determining discount points, especially discount start time. A nonlinear mathematical model is proposed to find optimal order quantity, discount points, and prices before the product's expiration date to maximize profit. The developed model provides the number of discounts such that the shortage will not be allowed before the expiration date. It is observed that determining a proper discount start time provides an optimized sales plan with higher profit. Moreover, the particle swarm optimization (PSO) and the genetic algorithm (GA) are applied to solve the problem. The Taguchi approach is used to find optimum control parameters of PSO and GA. To guarantee the validity of PSO and GA, the nonlinear model is solved by the BARON solver in GAMS software. The performance of the algorithms is evaluated based on the real values of parameters for two perishable products (i.e. Cheese and Mayonnaise Sauce) and some random test problems. The computational results demonstrate that the proposed GA outperforms the PSO algorithm.

Keywords

References

Reference
[1]          Harcar, T. and Karakaya, F. “A cross-cultural exploration of attitudes toward product expiration dates”, Psychology & Marketing, 22(4), pp. 353–371 (2005).
[2]        Minner, S. and Transchel, S. “Periodic review inventory-control for perishable products under service-level constraints”, OR spectrum, 32(4), pp. 979-996 (2010).
[3]        Kaya, O. and Polat, A.L. “Coordinated pricing and inventory decisions for perishable products”, OR spectrum, 39(2), pp. 589-606 (2017).
[4]        Nahmias, S. “Perishable inventory theory: a review”, Operations Research, 30(3), pp. 680-708 (1982).
[5]        Janssen, L., Claus, T., and Sauer, J. “Literature review of deteriorating inventory models by key topics from 2012 to 2015”, International Journal of Production Economics, 182(1), pp. 86-112 (2016).
[6]        Burwell, T.H., Dave, D.S., Fitzpatrick, K.E., and Roy, M.R. “An inventory model with planned shortages and price dependent demand”, Decision Sciences, 22(5), pp. 1187-1191 (1991).
[7]        Rajan, A., Rakesh, and Steinberg, R. “Dynamic pricing and ordering decisions by a monopolist”, Management science, 38(2), pp. 240-262 (1992).
[8]        Abad, P.L. “Optimal price and order size for a reseller under partial backordering”, Computers & Operations Research, 28(1), pp. 53-65 (2001).
[9]        Abad, P.L. “Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale”, European Journal of Operational Research, 144(3), pp. 677-685 (2003).
[10]      Mukhopadhyay, S., Mukherjee, R.N., and Chaudhuri, K.S. “Joint pricing and ordering policy for a deteriorating inventory”, Computers & Industrial Engineering, 47(4), pp. 339-349 (2004).
[11]      You, P.S. “Inventory policy for products with price and time-dependent demands”, Journal of the Operational Research Society, 56(7), pp. 870-873 (2005).
[12]      Sana, S.S. “Optimal selling price and lotsize with time varying deterioration and partial backlogging”, Applied Mathematics and computation, 217(1), pp. 185-194 (2010).
[13]      Avinadav, T., Herbon, A., and Spiegel, U. “Optimal inventory policy for a perishable item with demand function sensitive to price and time”, International Journal of Production Economics, 144(2), pp. 497-506 (2013).
[14]      Wee, H.M. “Economic production lot size model for deteriorating items with partial back-ordering”, Computers & Industrial Engineering, 24(3), pp. 449-458 (1993).
[15]      Wagner, H.M. and Whitin, T.M. “Dynamic version of the economic lot size model”, Management science, 5(1), pp. 89-96 (1958).
[16]      Ghare, P.M. and Schrader, G.F. “A model for exponentially decaying inventory”, Journal of industrial Engineering, 14(5), pp. 238-243 (1963).
[17]      Bhunia, A.K. and Maiti, M. “Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level”, Computers & operations research, 25(11), pp. 997-1006 (1998).
[18]      Wee, H.M. “A replenishment policy for items with a price-dependent demand and a varying rate of deterioration”, Production Planning & Control, 8(5), pp. 494-499 (1997).
[19]      Chakrabarty, T., Giri, B.C., and Chaudhuri, K.S. “An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: an extension of Philip's model”, Computers & Operations Research, 25(7), pp. 649-657 (1998).
[20]      Eilon, S. and Mallaya, R.V. Issuing and pricing policy of semi-perishables. in Proceedings of the 4th international conference on operational research. 1966. Wiley-Interscience.
[21]      Wee, H.M. “Joint pricing and replenishment policy for deteriorating inventory with declining market”, International journal of production economics, 40(2-3), pp. 163-171 (1995).
[22]      Federgruen, A. and Heching, A. “Combined pricing and inventory control under uncertainty”, Operations research, 47(3), pp. 454-475 (1999).
[23]      Chang, H.J., Teng, J.T., Ouyang, L.Y., and Dye, C.Y. “Retailer’s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging”, European Journal of Operational Research, 168(1), pp. 51-64 (2006).
[24]      Chen, L.M. and Sapra, A. “Joint inventory and pricing decisions for perishable products with two‐period lifetime”, Naval Research Logistics (NRL), 60(5), pp. 343-366 (2013).
[25]      Taleizadeh, A.A., Satarian, F., and Jamili, A. “Optimal multi-discount selling prices schedule for deteriorating product”, Scientia Iranica E, 22(6), pp. 2595-2603 (2015).
[26]      Adenso-Díaz, B., Lozano, S., and Palacio, A. “Effects of dynamic pricing of perishable products on revenue and waste”, Applied Mathematical Modelling, 45, pp. 148-164 (2017).
[27]      Feng, L., Chan, Y.L., and Cárdenas-Barrón, L.E. “Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date”, International Journal of Production Economics, 185, pp. 11-20 (2017).
[28]      Yao, D. “Joint pricing and inventory control for a stochastic inventory system with Brownian motion demand”, IISE Transactions, 49(12), pp. 1101-1111 (2017).
[29]      Dobson, G., Pinker, E.J., and Yildiz, O. “An EOQ model for perishable goods with age-dependent demand rate”, European Journal of Operational Research, 257(1), pp. 84-88 (2017).
[30]      Chua, G.A., Mokhlesi, R., and Sainathan, A. “Optimal discounting and replenishment policies for perishable products”, International Journal of Production Economics, 186, pp. 8-20 (2017).
[31]      Kaya, O. and Rahimi Ghahroodi, S. “Inventory control and pricing for perishable products under age and price dependent stochastic demand”, Mathematical Methods of Operations Research, 88(1), pp. 1-35 (2018).
[32]      Agi, M.A. and Soni, H.N. “Joint pricing and inventory decisions for perishable products with age-, stock-, and price-dependent demand rate”, Journal of the Operational Research Society, 71(1), pp. 85-99 (2019).
[33]      Khan, M.A.A., Shaikh, A.A., Panda, G.C., Konstantaras, I., and Taleizadeh, A.A. “Inventory system with expiration date: Pricing and replenishment decisions”, Computers & Industrial Engineering, 132, pp. 232-247 (2019).
[34]      Wei, J., Liu, Y., Zhao, X., and Yang, X. “Joint optimization of pricing and inventory strategy for perishable product with the quality and quantity loss”, Journal of Industrial and Production Engineering, 37(1), pp. 23-32 (2020).
[35]      Dye, C.Y. “Optimal joint dynamic pricing, advertising and inventory control model for perishable items with psychic stock effect”, European Journal of Operational Research, 283(2), pp. 576-587 (2020).
[36]      Soni, H.N. “Joint Pricing and Inventory Policies for Perishable Items with Price Discount based on Freshness Index”, Turkish Journal of Computer and Mathematics Education, 12(11), pp. 1954-1963 (2021).
[37]      Kaya, O. and Bayer, H. “Pricing and lot-sizing decisions for perishable products when demand changes by freshness”, Journal of Industrial & Management Optimization, 17(6), pp. 3113 (2021).
[38]      Tawarmalani, M. and Sahinidis, N.V. “GAMS/BARON: A Tutorial and Empirical Performance Analysis”, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming, ( ), pp. 313-401 (2002).
[39]      Bratton, D. and Kennedy, J. Defining a standard for particle swarm optimization. in Swarm Intelligence Symposium, 2007. SIS 2007. IEEE.
[40]      Snkar, K.P. “Classification and learning using genetic algorithms”, Springer, (2007).
Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 16 January 2022

Files

Share

How to cite

Statistics